Solve frac{N_{A}*10^6}{12}

$$\frac { N _ { A } \times 10 ^ { 6 } } { 12 }$$

Evaluate

$$\frac{250000N_{A}}{3}$$

Solution Steps

Calculate 10 to the power of 6 and get 1000000.

$$\frac{N_{A}\times 1000000}{12}$$

Divide N_{A}\times 1000000 by 12 to get N_{A}\times \frac{250000}{3}.

$$N_{A}\times \frac{250000}{3}$$

Differentiate w.r.t. N_A

$$\frac{250000}{3} = 83333\frac{1}{3} = 83333.33333333333$$

Steps Using Definition of a Derivative

Calculate 10 to the power of 6 and get 1000000.

$$\frac{\mathrm{d}}{\mathrm{d}N_{A}}(\frac{N_{A}\times 1000000}{12})$$

Divide N_{A}\times 1000000 by 12 to get N_{A}\times \frac{250000}{3}.

$$\frac{\mathrm{d}}{\mathrm{d}N_{A}}(N_{A}\times \frac{250000}{3})$$

The derivative of ax^{n} is nax^{n-1}.

$$\frac{250000}{3}N_{A}^{1-1}$$

Subtract 1 from 1.

$$\frac{250000}{3}N_{A}^{0}$$

For any term t except 0, t^{0}=1.

$$\frac{250000}{3}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{250000}{3}$$